Solve for $x$ and $y$ using elimination. ${x+6y = 48}$ ${x+5y = 41}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-x-6y = -48}$ $x+5y = 41$ Add the top and bottom equations together. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x+6y = 48}\thinspace$ to find $x$ ${x + 6}{(7)}{= 48}$ $x+42 = 48$ $x+42{-42} = 48{-42}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {x+5y = 41}\thinspace$ and get the same answer for $x$ : ${x + 5}{(7)}{= 41}$ ${x = 6}$